Posted by **Grace** on Thursday, January 19, 2012 at 3:09am.

The figure shows a 10 x 10 square centered at the origin. The darker-shaded square is the image of this square, dilated by a factor of 0.8 and rotated about the origin by exactly the number of degrees, , so that its corners touch the sides of the parent square. The corners of the rotated square divide the sides of the 10 x 10 square into segments of length a and b.

Use the fact that a and b add up to 10 to find the value of theta.

- Precalc -
**drwls**, Thursday, January 19, 2012 at 6:28am
Not without the figure. I cannot visualize the situation from your verbal description. Perhaps another teacher can.

- Precalc -
**Steve**, Thursday, January 19, 2012 at 11:09am
You end up with a rotated square of side 8, surrounded by 4 right triangles of sides x and 10-x.

x^2 + (10-x)^2 = 64

x^2 + 100 - 20x + x^2 = 64

2x^2 - 20x + 36 = 0

x^2 - 10x + 18 = 0

x = 5 ± √7 = 2.35 or 7.65

if we let x be the smaller value, then

tanθ = 2.35/7.65 = 0.307

θ = 17°

- Precalc -
**Grace**, Thursday, January 19, 2012 at 1:03pm
Thank you so so so much! I've been stuck on this for hours!

## Answer this Question

## Related Questions

Precalculus - The figure shows a 10 x 10 square centered at the origin. The ...

Geometry - Dilation of a square - The preimage of square ABCD has its center at...

Matrices - A triangle has vertices (1, 4), (1, 1), and (−3, 1). The ...

Algebra - I'm stuck!! Can someone please help me with this problem?? A triangle ...

Algebra - I need help with two math problems. 1. A triangle has vertices (1, 4...

Geometry - Calculate the area of the shaded region in the figure shown. the ...

Math - The point A (-7, 5) is reflected over the line x = -5, and then is ...

geometry - how do i find the probability that a point in a figue lies in the ...

math - The figure shows 2 similar squares, A and B which overlap each other. The...

Math word problem - A small circular pool is enclosed in a square. Find the area...